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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Row and column finite matrices


Author: Pace P. Nielsen
Journal: Proc. Amer. Math. Soc. 135 (2007), 2689-2697
MSC (2000): Primary 16S50; Secondary 16P40
Published electronically: February 9, 2007
MathSciNet review: 2317941
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Abstract: Consider the ring of all $ \kappa\times \kappa$ column finite matrices over a ring $ R$. We prove that each such matrix is conjugate to a row and column finite matrix if and only if $ R$ is right Noetherian and $ \kappa$ is countable. We then demonstrate that one can perform this conjugation on countably many matrices simultaneously. Some applications and limitations are given.


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Additional Information

Pace P. Nielsen
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
Email: pace_nielsen@hotmail.com

DOI: https://doi.org/10.1090/S0002-9939-07-08790-4
Keywords: Row and column finite matrices, endomorphism ring, vector space
Received by editor(s): November 19, 2005
Received by editor(s) in revised form: May 12, 2006
Published electronically: February 9, 2007
Communicated by: Martin Lorenz
Article copyright: © Copyright 2007 American Mathematical Society